Séminaire Lotharingien de Combinatoire, 93B.40 (2025), 12 pp.
Alexander E. Black, Sophie Rehberg and Raman Sanyal
Poset Permutahedra
Abstract.
Poset permutahedra are an amalgamation of order polytopes and permutahedra. We show that poset
permutahedra give a unifying perspective on several recent classes of polytopes that occurred, for
example, in connection with colorful subdivisions of polygons and Hessenberg varieties. As with
order polytopes, the geometry and the combinatorics of poset permutahedra can be completely
described in terms of the underlying poset. As applications of our results, we give a combinatorial
description of the h-vectors of the partitioned permutahedra of Horiguchi et al. and
poset generalizations of Landau's score sequences of tournaments. To prove our results, we show that
poset permutahedra arise from order polytopes via the fiber polytope construction of Billera and
Sturmfels.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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